So it seems that the name of the app shown in a Mac Catalyst app comes from the "Product Name" build setting for your target. I changed that from MyCoolApp to My Cool App and I started seeing the results I wanted.
I find it odd that the app display name comes from the resulting .app name and the executable name and not the "Bundle display name" from Info.plist.
Maybe this will help someone else.
Topic:
App & System Services
SubTopic:
General
Tags: